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Efficient robust estimation of regression models

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Author Info
Cizek, Pavel (Tilburg University, Center for Economic Research)

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Abstract

This paper introduces a new class of regression estimators robust to outliers, measurement errors, and other data irregularities. The estimators are based on the twostep least weighted squares method, where weights are adaptively computed using the empirical distribution function of regression residuals obtained from an initial robust fit. The asymptotic distribution of the proposed estimators is derived under general conditions, allowing for time-series applications. Further, it is shown that the breakdown point of the proposed estimators equals that of the initial robust estimate. The main contribution of the work is that the proposed two-step procedures combine several desirable properties, which different existing estimators posses separately, but not jointly. These properties are asymptotic efficiency if the errors are normally distributed, high breakdown point achieved without rejecting (trimming) of observations, and independence of auxiliary tuning parameters. A Monte Carlo study shows that the two-step least weighted squares outperform in most situations both least squares and existing robust estimators in finite samples.

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Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 8.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:20068

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Web page: http://center.uvt.nl

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Related research
Keywords: least weighted squares; linear regression; robust statistics; two-step estimation;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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    Other versions:
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    Other versions:
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